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LinKer
Syntax
LinKer(M:MAT):LIST
LinKerModP(M:MAT):LIST
where M is a matrix over Q or Z.
Summary
find the kernel of a matrix
Description
The first function returns a list whose components are lists
representing a Z-basis for the kernel of M. Calling the function
twice on the same input will not necessarily produce the same output,
though in each case, a basis for the kernel is produced.
The second function returns a list whose components are lists
representing a basis for the kernel of M over the current field of
coefficients.
example
M := Mat([[1,2,3,4],[5,6,7,8],[9,10,11,12]]);
LinKer(M);
[[1, -1, -1, 1], [0, 1, -2, 1]]
-------------------------------
M*Transposed(Mat(It));
Mat[
[0, 0],
[0, 0],
[0, 0]
]
-------------------------------
Use Z/(3)[x];
LinKerModP(M);
[[1, 1, 1, 0], [0, -1, -1, -1]]
-------------------------------
M*Transposed(Mat(It));
Mat([
[0, 0],
[0, 0],
[0, 0]
])
-------------------------------
See Also